-3y^2-23y+14=0

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Solution for -3y^2-23y+14=0 equation: 


Simplifying
-3y2 + -23y + 14 = 0

Reorder the terms:
14 + -23y + -3y2 = 0

Solving
14 + -23y + -3y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4.666666667 + 7.666666667y + y2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 7.666666667y + 4.666666667 + y2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 7.666666667y + y2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 7.666666667y + y2 = 0 + 4.666666667
7.666666667y + y2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
7.666666667y + y2 = 4.666666667

The y term is 7.666666667y.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667y + 14.69444445 + y2 = 4.666666667 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667y + y2 = 4.666666667 + 14.69444445

Combine like terms: 4.666666667 + 14.69444445 = 19.361111117
14.69444445 + 7.666666667y + y2 = 19.361111117

Factor a perfect square on the left side:
(y + 3.833333334)(y + 3.833333334) = 19.361111117

Calculate the square root of the right side: 4.400126261

Break this problem into two subproblems by setting 
(y + 3.833333334) equal to 4.400126261 and -4.400126261.


Subproblem 1
y + 3.833333334 = 4.400126261

Simplifying
y + 3.833333334 = 4.400126261

Reorder the terms:
3.833333334 + y = 4.400126261

Solving
3.833333334 + y = 4.400126261

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + y = 4.400126261 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + y = 4.400126261 + -3.833333334
y = 4.400126261 + -3.833333334

Combine like terms: 4.400126261 + -3.833333334 = 0.566792927
y = 0.566792927

Simplifying
y = 0.566792927


Subproblem 2
y + 3.833333334 = -4.400126261

Simplifying
y + 3.833333334 = -4.400126261

Reorder the terms:
3.833333334 + y = -4.400126261

Solving
3.833333334 + y = -4.400126261

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + y = -4.400126261 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + y = -4.400126261 + -3.833333334
y = -4.400126261 + -3.833333334

Combine like terms: -4.400126261 + -3.833333334 = -8.233459595
y = -8.233459595

Simplifying
y = -8.233459595


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.566792927, -8.233459595}

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